Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States
Abstract
Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations typically provide more accurate values of the excitation energy of Rydberg states than time-dependent density functional theory approaches, but their performance with respect to excited-state properties such as the dipole moment remains largely unexplored as existing benchmarks are limited to the lowest excited state. Here, orbital-optimized density functional calculations with a plane-wave basis set are used to compute the dipole moment of several Rydberg states of a set of small molecules. Plane waves provide a flexible representation of diffuse Rydberg orbitals, whereas commonly used atomic orbitals basis sets are found to yield significant discrepancies in the magnitude and orientation of the dipole moment, even when diffuse functions are included and the excitation energy agrees well with the plane-wave results. The generalized gradient approximation functional PBE used in combination with the plane-wave representation of the orbitals gives good agreement with higher-level coupled-cluster calculations performed with sufficiently diffuse basis sets, when the latter are available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction generally leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic −1/r dependence of the effective Kohn--Sham potential.
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BibTeX
@misc{restaino2026excitedstate,
title = {{Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States}},
author = {Lorenzo Restaino and Jukka John and Diego Llorena Prieto and Yorick Leonard Adrian Schmerwitz and Elvar Örn Jónsson and Gianluca Levi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.12272},
eprint = {2606.12272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.12272},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States
AU - Lorenzo Restaino
AU - Jukka John
AU - Diego Llorena Prieto
AU - Yorick Leonard Adrian Schmerwitz
AU - Elvar Örn Jónsson
AU - Gianluca Levi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2606.12272
UR - https://arxiv.org/abs/2606.12272
AB - Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations typically provide more accurate values of the excitation energy of Rydberg states than time-dependent density functional theory approaches, but their performance with respect to excited-state properties such as the dipole moment remains largely unexplored as existing benchmarks are limited to the lowest excited state. Here, orbital-optimized density functional calculations with a plane-wave basis set are used to compute the dipole moment of several Rydberg states of a set of small molecules. Plane waves provide a flexible representation of diffuse Rydberg orbitals, whereas commonly used atomic orbitals basis sets are found to yield significant discrepancies in the magnitude and orientation of the dipole moment, even when diffuse functions are included and the excitation energy agrees well with the plane-wave results. The generalized gradient approximation functional PBE used in combination with the plane-wave representation of the orbitals gives good agreement with higher-level coupled-cluster calculations performed with sufficiently diffuse basis sets, when the latter are available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction generally leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic −1/r dependence of the effective Kohn--Sham potential.
ER -